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Transcendence conjectures about periods of modular forms and rational structures on spaces of modular forms

  • Winfried Kohnen
Article

Abstract

The conjecture is made that the rational structures on spaces of modular forms coming from the rationality of Fourier coefficients and the rationality of periods are not compatible. A consequence would be that ζ(2k-1)/π 2k-1 (ζ(s)=Riemann zeta function;k∈ℕ,k≥2) is irrational or even transcendental.

Keywords

Modular forms rational structures periods transcendence Riemann zeta function 

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References

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    Bertrand D, Varietes abeliennes et formes lineaires d' integrales elliptiques, in:Sém. de Théorie des Nombres, Paris 1979–80 (ed. M.-J. Bertin), pp. 15–27,Progress in Maths.12 Birkhäuser, Boston-Basel-Stuttgart 1981.Google Scholar
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    Beukers F, Irrationality proofs using modular forms,Soc. Math. de France, Astérisque 147–148 (1987), pp. 271–283.Google Scholar
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    Kohnen W and Zagier D, Modular forms with rational periods, in:Modular Forms (ed. R A Rankin) pp. 197–249, (Chichester: Ellis Horwood) 1984.Google Scholar

Copyright information

© Indian Academy of Science 1989

Authors and Affiliations

  • Winfried Kohnen
    • 1
    • 2
  1. 1.Mathematisches Institut der Universität MünsterMünsterFederal Republic of Germany
  2. 2.Max-Planck-Institut für MathematikBonn 3Federal Republic of Germany

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